[racket-dev] Floating-Point Compliance Testing
Tested it too and got an interesting result. On a 32bit linux its:
+nan.0
+nan.0
+nan.0
+nan.0
+nan.0
+nan.0
+nan.0
+nan.0
so, completely wrong. But on a 64bit Linux its correct if i use the 64bit
racket version. When i try the 32bit build i get the wrong results again.
I think you can blame it on 32 implementation of racket/libc/compiler or
whatever. Not on the actual cpu in use because the hardware was always the
same (2 identical computers, identical OS + version, only 32bit in one, 64
in the other).
Tobias
On Fri, 08 Feb 2013 19:07:53 +0100, Neil Toronto <neil.toronto at gmail.com>
wrote:
> Back on list.
>
> A lot of things point to general sloppiness in either the FPU or C
> libraries, but I'd like more information just in case. Can you reply
> with the values of the following expressions on the Athlon?
>
> (flexpt -1001.0 -1.3407807929942596e+154)
> (flexpt -1001.0 1.3407807929942596e+154)
> (flexpt -0.1 -1.3407807929942596e+154)
> (flexpt -0.1 1.3407807929942596e+154)
> (flexpt -744.4400719213812 -1.3407807929942596e+154)
> (flexpt -744.4400719213812 1.3407807929942596e+154)
> (flexpt -1.0 -1.3407807929942596e+154)
> (flexpt -1.0 1.3407807929942596e+154)
>
> You should get these values:
>
> 0.0 +inf.0 +inf.0 0.0 0.0 +inf.0 1.0 1.0
>
> I think these are cases Racket handles specially instead of handing off
> to C's `pow' on platforms where we know `pow' handles them wrongly. We
> might need to ask Matthew to expand that set of platforms.
>
> Small rounding errors like this:
>
> ((fl*/error -6.87181640380727e-156 2.3341566035927725e-153)
> 0.7079979032237692)
>
> which are only 1 bit off, are probably the cause of these errors:
>
> ((fl2log 1.5124390004859715e-308 0.0) 4294967296.220986)
> ((fl2log1p 3.799205740343036e+246 1.4492752004468653e+230)
> 549755813887.9473))
>
> `fl2log' and `fl2log1p' are 103-ish-bit logarithm implementations used
> in certain tricky subdomains of a few special functions. They assume
> arithmetic is always correct and are very sensitive to rounding errors.
> You're getting about 65-bit output precision for certain inputs. We can
> almost certainly blame the FPU because IEEE 754 requires arithmetic to
> be implemented and correctly rounded.
>
> IEEE 754 only *recommends* typical irrational functions. When they're
> not implemented in hardware, C libraries compute them in software. So I
> don't know whether these and others are the FPU's or C library's fault:
>
> ((flsin 2.5489254492488616e+52) 22637349860729424.0)
> ((flcos 3.91520018229574e+49) 6369061509154398.0)
> ((fltan 1.6614020610450763e+21) 9158003261155244.0)
> ((flexp 16.938769136983012) 7.0)
> ((flexp 282.52374429474406) 102.0)
> ((flexp -10.0) 4.0)
> ((flexp -708.3964185322641) 124.0)
>
> These errors come from not doing argument reductions carefully enough.
> The trigonometric functions probably don't compute x % 2*pi using a
> high-precision 2*pi when x is large. They seem to be correct enough when
> x is small, though.
>
> The exponential function wasn't tested well at the boundaries of its
> domain:
>
> ((flexp 709.782712893384) +inf.0)
>
> 709.782712893384 is (fllog +max.0), and (flexp (fllog +max.0)) should be
> near +max.0, not (as I suspect) +inf.0.
>
> I don't know whether Racket should do anything about these errors. I
> don't think it would be too hard to do something like Java's StrictMath,
> but it would take time.
>
> In the meantime, don't use the Athlon for serious numerical computation.
>
> Neil ⊥
>
> On 02/08/2013 12:13 AM, Laurent wrote:
>> Hi Neil,
>>
>> Interaction in a terminal is attached, using Racket 5.3.2.3.
>>
>> Some details about my machine:
>> Linux 3.2.0-37-generic-pae #58-Ubuntu SMP Thu Jan 24 15:51:02 UTC 2013
>> i686 athlon i386 GNU/Linux
>>
>> In particular, I use a 32bits Ubuntu 12.04.2 on a 686 processor, if
>> that's of any interest.
>>
>> Cheers,
>> Laurent
>>
>>
>>
>>
>> On Fri, Feb 8, 2013 at 1:15 AM, Neil Toronto <neil.toronto at gmail.com
>> <mailto:neil.toronto at gmail.com>> wrote:
>>
>> On 02/07/2013 12:09 PM, Laurent wrote:
>>
>> On Thu, Feb 7, 2013 at 5:50 PM, Neil Toronto
>> <neil.toronto at gmail.com <mailto:neil.toronto at gmail.com>
>> <mailto:neil.toronto at gmail.com
>> <mailto:neil.toronto at gmail.com>__>> wrote:
>>
>> Today is not that day, but thanks for asking about this
>> anyway. :)
>>
>>
>> On one machine with Ubuntu 12.10, I get no error, but on another
>> machine
>> with Ubuntu 12.04, I get more than 14000 errors, many of them
>> being
>> +inf.0 and other numbers with big exponents (is my machine
>> really that
>> bad?).
>> Is this exactly the kind of reply you want to avoid for now or
>> are you
>> interested in a report?
>>
>>
>> Alrighty, you've piqued my interest. Better send it off-list,
>> though. :)
>>
>> Neil ⊥
>
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--
---------------------------------------------------------
Tobias Hammer
DLR / Institute of Robotics and Mechatronics
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Tel.: 08153/28-1487
Mail: tobias.hammer at dlr.de